- Practice Problems
- Assignment Problems
- Show all Solutions/Steps/ etc.
- Hide all Solutions/Steps/ etc.
- Solutions and Solution Sets
- Applications of Linear Equations
- Preliminaries
- Graphing and Functions
- Calculus II
- Calculus III
- Differential Equations
- Algebra & Trig Review
- Common Math Errors
- Complex Number Primer
- How To Study Math
- Cheat Sheets & Tables
- MathJax Help and Configuration
- Notes Downloads
- Complete Book
- Practice Problems Downloads
- Complete Book - Problems Only
- Complete Book - Solutions
- Assignment Problems Downloads
- Other Items
- Get URL's for Download Items
- Print Page in Current Form (Default)
- Show all Solutions/Steps and Print Page
- Hide all Solutions/Steps and Print Page

## Section 2.2 : Linear Equations

Solve each of the following equations and check your answer.

- \(4x - 7\left( {2 - x} \right) = 3x + 2\) Solution
- \(2\left( {w + 3} \right) - 10 = 6\left( {32 - 3w} \right)\) Solution
- \(\displaystyle \frac{{4 - 2z}}{3} = \frac{3}{4} - \frac{{5z}}{6}\) Solution
- \(\displaystyle \frac{{4t}}{{{t^2} - 25}} = \frac{1}{{5 - t}}\) Solution
- \(\displaystyle \frac{{3y + 4}}{{y - 1}} = 2 + \frac{7}{{y - 1}}\) Solution
- \(\displaystyle \frac{{5x}}{{3x - 3}} + \frac{6}{{x + 2}} = \frac{5}{3}\) Solution

## Word Problems on Linear Equations

## Step-by-step application of linear equations to solve practical word problems:

1. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

More solved examples with detailed explanation on the word problems on linear equations.

How to Solve Linear Equations?

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

Worksheet on Word Problems on Linear Equation

7th Grade Math Problems 8th Grade Math Practice From Word Problems on Linear Equations to HOME PAGE

## New! Comments

- Preschool Activities
- Kindergarten Math
- 1st Grade Math
- 2nd Grade Math
- 3rd Grade Math
- 4th Grade Math
- 5th Grade Math
- 6th Grade Math
- 7th Grade Math
- 8th Grade Math
- 9th Grade Math
- 10th Grade Math
- 11 & 12 Grade Math
- Concepts of Sets
- Probability
- Boolean Algebra
- Math Coloring Pages
- Multiplication Table
- Cool Maths Games
- Math Flash Cards
- Online Math Quiz
- Math Puzzles
- Binary System
- Math Dictionary
- Conversion Chart
- Homework Sheets
- Math Problem Ans
- Free Math Answers
- Printable Math Sheet
- Funny Math Answers
- Employment Test
- Math Patterns
- Link Partners

© and ™ math-only-math.com. All Rights Reserved. 2010 - 2022.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## Unit 6: Lesson 3

- Solving linear equations and linear inequalities | Lesson
- Understanding linear relationships | Lesson
- Linear inequality word problems | Lesson
- Graphing linear equations | Lesson
- Systems of linear inequalities word problems | Lesson
- Solving systems of linear equations | Lesson

## Systems of linear equations word problems | Lesson

What are systems of linear equations word problems, and how frequently do they appear on the test.

## How do I solve systems of linear equations word problems?

Systems of equations examples, how do i write systems of linear equations.

- Select variables to represent the unknown quantities.
- Using the given information, write a system of two linear equations relating the two variables.
- Solve the system of linear equations using either substitution or elimination.

## Let's look at an example!

- (Choice A) c − 1 = b 4 b + 6 c = 31 \begin{aligned} c-1 &= b \\ \\ 4b+6c &=31 \end{aligned} c − 1 4 b + 6 c = b = 3 1 A c − 1 = b 4 b + 6 c = 31 \begin{aligned} c-1 &= b \\ \\ 4b+6c &=31 \end{aligned} c − 1 4 b + 6 c = b = 3 1
- (Choice B) c + 1 = b 4 b + 6 c = 31 \begin{aligned} c+1 &= b \\ \\ 4b+6c &=31 \end{aligned} c + 1 4 b + 6 c = b = 3 1 B c + 1 = b 4 b + 6 c = 31 \begin{aligned} c+1 &= b \\ \\ 4b+6c &=31 \end{aligned} c + 1 4 b + 6 c = b = 3 1
- (Choice C) c − 1 = b 6 b + 4 c = 31 \begin{aligned} c-1 &= b \\ \\ 6b+4c &=31 \end{aligned} c − 1 6 b + 4 c = b = 3 1 C c − 1 = b 6 b + 4 c = 31 \begin{aligned} c-1 &= b \\ \\ 6b+4c &=31 \end{aligned} c − 1 6 b + 4 c = b = 3 1
- (Choice D) c + 1 = b 6 b + 4 c = 31 \begin{aligned} c+1 &= b \\ \\ 6b+4c &=31 \end{aligned} c + 1 6 b + 4 c = b = 3 1 D c + 1 = b 6 b + 4 c = 31 \begin{aligned} c+1 &= b \\ \\ 6b+4c &=31 \end{aligned} c + 1 6 b + 4 c = b = 3 1
- (Choice A) 1 1 1 1 A 1 1 1 1
- (Choice B) 2 2 2 2 B 2 2 2 2
- (Choice C) 3 3 3 3 C 3 3 3 3
- (Choice D) 4 4 4 4 D 4 4 4 4
- Your answer should be
- an integer, like 6 6 6 6
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a multiple of pi, like 12 pi 12\ \text{pi} 1 2 pi 12, space, start text, p, i, end text or 2 / 3 pi 2/3\ \text{pi} 2 / 3 pi 2, slash, 3, space, start text, p, i, end text

## Want to join the conversation?

## Writing Systems of Linear Equations from Word Problems

(i) There are two different quantities involved: for instance, the number of adults and the number of children, the number of large boxes and the number of small boxes, etc. (ii) There is a value associated with each quantity: for instance, the price of an adult ticket or a children's ticket, or the number of items in a large box as opposed to a small box.

Here are some steps to follow:

Understand all the words used in stating the problem. Understand what you are asked to find. Familiarize the problem situation.

2. Translate the problem to an equation.

Assign a variable (or variables) to represent the unknown. Clearly state what the variable represents.

3. Carry out the plan and solve the problem.

Use substitution , elimination or graphing method to solve the problem.

The admission cost for 12 children and 3 adults was $ 162 . The admission cost for 8 children and 3 adults was $ 122 .

2 . Translate the problem to an equation.

Let x represent the admission cost for each child. Let y represent the admission cost for each adult. The admission cost for 12 children plus 3 adults is equal to $ 162 . That is, 12 x + 3 y = 162 . The admission cost for 8 children plus 3 adults is equal to $122. That is, 8 x + 3 y = 122 .

3 . Carry out the plan and solve the problem.

Subtract the second equation from the first. 12 x + 3 y = 162 8 x + 3 y = 122 _ 4 x = 40 x = 10 Substitute 10 for x in 8 x + 3 y = 122 . 8 ( 10 ) + 3 y = 122 80 + 3 y = 122 3 y = 42 y = 14 Therefore, the cost of admission for each child is $ 10 and each adult is $ 14 .

## Download our free learning tools apps and test prep books

4.9/5.0 Satisfaction Rating over the last 100,000 sessions. As of 4/27/18.

*See complete details for Better Score Guarantee.

Award-Winning claim based on CBS Local and Houston Press awards.

Varsity Tutors does not have affiliation with universities mentioned on its website.

## IMAGES

## VIDEO

## COMMENTS

Section 2.2 : Linear Equations · 4x−7(2−x)=3x+2 4 x − 7 ( 2 − x ) = 3 x + 2 Solution · 2(w+3)−10=6(32−3w) 2 ( w + 3 ) − 10 = 6 ( 32 − 3 w )

Examples on Solving Linear Equations: · 1. Solve: (2x + 5)/(x + 4) = 1. Solution: (2x + 5)/(x + 4) = 1. ⇒ 2x + 5 = 1(x + 4) · 2. Solve: 6x - 19 = 3x - 10.

Word Problems on Linear Equations · Then the other number = x + 9. Let the number be x. · 2.The difference between the two numbers is 48. · 3. The length of a

Watch Sal work through a basic Linear equations word problem. ... You can solve a question any way you want as long as you're sure it's

Select variables to represent the unknown quantities. · Using the given information, write a system of two linear equations relating the two variables. · Solve

GRADE 7:SOLVING PROBLEMS INVOLVING LINEAR EQUATIONS IN ONE VARIABLEGRADE 7 PLAYLISTFirst Quarter: https://tinyurl.com/yyzdequa Second Qu...

Learn how to solve a word problem by writing an equation to model the situation. In this video, we use the linear equation 210(t-5) = 41,790

1.20: Word Problems for Linear Equations · 5x=60 · x · x=605=12 · 13. · 2x−5=13 · x · 2x=13+5, so that 2x=18 · x=182=9

1. Solve for x: 3x - 12 = 0. basket1aa · 2. Solve for m: 2(m + 6) = 48. purplegirl1 · 3. Solve for x: 3(2x - 1) - 10 = 8 + 5x. basket2 · 4. Solve for x: 8x + 9 -

Writing Systems of Linear Equations from Word Problems · 1. Understand the problem. Understand all the words used in stating the problem. Understand what you are